A Telescoping Arctangent

★ 7/10trigonometrysequencesTrigonometric IdentitiesTelescoping

Problem

Compute

tan⁡(arctan⁡2+arctan⁡222+⋯+arctan⁡2122).\tan\left(\arctan 2 + \arctan\frac{2}{2^2} + \cdots + \arctan\frac{2}{12^2}\right).

Answer

Solution

Difficulty7/10
Topicstrigonometry, sequences, Trigonometric Identities, Telescoping

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